We finished off the preceding week’s work by solving an inequality involving the absolute value function and a rational function. Also we did an example showing how to* bound* the absolute value of a rational function on an interval (using the *triangle inequality* and the *reverse triangle inequality*).

We began a new chapter: *Limits & Continuity*. We gave the – definition of the limit of a function. We did a few examples. We defined *left- and right- hand limits* and proved that a limit exists if and only if its left- and right-hand limits exist and are equal.

In one example, we showed a limit did not exist as the left- and right-hand limits did not agree. We then did two examples using the – definition but noted we wouldn’t always have to do this due to the *Calculus of Limits*. We wrote down the five results and said we will prove the first and second, put the third and fourth on the webpage, and do a sketch of the fifth.

**Problems**

*You need to do exercises – all of the following you should be able to attempt. Do as many as you can/ want in the following order of most beneficial:*

*Wills’ Exercise Sheets
*

Q.7, 8, 9 from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise1.pdf

*More exercise sheets*

Q. 3, 4 from Problems

*Past Exam Papers*

Q. 1(a), 2 from http://booleweb.ucc.ie/ExamPapers/exams2010/MathsStds/MS2001Sum2010.pdf

Q . 1(a), 2(a) from http://booleweb.ucc.ie/ExamPapers/exams2009/MathsStds/MS2001s09.pdf

Q. 1(a), 2 from http://booleweb.ucc.ie/ExamPapers/exams2009/MathsStds/Autumn/MS2001A09.pdf

Q. 1(a) from http://booleweb.ucc.ie/ExamPapers/exams2008/Maths_Stds/MS2001Sum08.pdf

Q. 1(a), 2(a)(i), (b) from http://booleweb.ucc.ie/ExamPapers/Exams2008/MathsStds/MS2001a08.pdf

Q. 2 from http://booleweb.ucc.ie/ExamPapers/exams2007/Maths_Stds/MS2001Sum2007.pdf

Q. 1, 2(a) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/MS2001Sum06.pdf

Q. 1, 2(a) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/Autumn/ms2001Aut.pdf

Q. 1, 2(a) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001.pdf

Q. 1, 2(a) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001Aut05.pdf

Q. 1(a), 2(a), 3(b) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/MS2001aut.pdf

Q. 1(a), 2 from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/ms2001s2004.pdf

Q. 1(a), 2(a), 3 from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/MS2001.pdf

Q. 1(a), 3 from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/ms2001aut.pdf

Q. 1, 2(a) from http://booleweb.ucc.ie/ExamPapers/exams2002/Maths_Stds/ms2001.pdf

Q. 1(a), 2(a), 3 from http://booleweb.ucc.ie/ExamPapers/exams2001/Maths_studies/MS2001Summer01.pdf

Q. 1(a), 2 from http://booleweb.ucc.ie/ExamPapers/exams/Mathematical_Studies/MS2001.pdf

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